a)
To calculate: The present value of the payments at an ordinary
Introduction:
The present value of the cash flows in the future with a particular discount rate is the present value of annuity. The repeating payment that is made at the starting of every period is the annuity due.
a)
Answer to Problem 46QP
- The present value of
annuity is $59,890.65. - The present value annuity due is $64,681.90.
Explanation of Solution
Given information:
Person X is going to receive $15,000 per year for 5 years. The correct interest rate is 8%
Suppose the payments are in the form of an ordinary
Formula to compute the present value annuity for sixty months:
Note: C denotes the annual cash flow, r denotes the rate of exchange, and t denotes the time period.
Compute the present value annuity:
Hence, the present value of annuity is $59,890.65.
Formula to compute the present value of annuity due:
Note: The PVA is the present value of annuity and r is the rate of interest.
Compute the present value of annuity due:
Hence, the present value of annuity due is $64,681.90.
b)
To calculate: The
Introduction:
The value of a group of recurring payments at a particular date in the future is the future vale of annuity.
b)
Answer to Problem 46QP
- The future value of
annuity is $87,999.01. - The future value of annuity due is $95,038.94.
Explanation of Solution
The future value of the
Formula to calculate the future value annuity:
Note: C denotes the annual cash flow or annuity payment, r denotes the rate of interest, and t denotes the number of payments.
Compute the future value annuity:
Hence, the future value of annuity is $87,999.01.
Formula to compute the future value of annuity due:
Note: The FVA is the future value of annuity and r is the rate of interest.
Compute the present value of annuity due:
Hence, the future value of annuity due is $95,038.94.
c)
To find: The highest present value, the ordinary
c)
Answer to Problem 46QP
The present value of
Explanation of Solution
If the rate of interest is positive, then the present value of the
If the rate of interest is positive, then the future value of the annuity due will be the highest when compared to the future value of annuity. Every cash flow is made a year before; therefore, every cash flow gets an extra period of compounding.
Hence, the present value of annuity due has the highest present value and the future value of annuity due has the highest future value.
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